Properties exponential functions

Introduction: A function of the form $y(x)=a^x$, where $a$ ($a \neq 1)$ is a positive number, is called an exponential function with base $a$.

Theorem: Exponential functions have the following properties:

1. $a^x\cdot a^y=a^{x+y}$
2. $a^{-x}=\dfrac{1}{a^x}$
3. $\dfrac{a^x}{a^y}=a^{x-y}$
4. $(a^x)^y=a^{xy}$
5. $a^0=1$

Remark: Compare these properties with the Properties power functions.